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seen Apr 20 at 23:35

Jul
2
awarded  Curious
Apr
17
asked difference of the values of a function is an integral
Oct
28
awarded  Nice Question
Apr
21
asked relation between Holder continuous and weakly differentiable for the coefficients of a pde
Apr
17
revised matrix with distinct bounded eigen values is bounded?
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Apr
16
revised matrix with distinct bounded eigen values is bounded?
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Apr
15
asked matrix with distinct bounded eigen values is bounded?
Mar
22
revised Existence of the degenerate elliptic PDE coefficient condition
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Mar
11
comment Existence of the degenerate elliptic PDE coefficient condition
ok, but the condition saying $c \leq c_0 <0$ doesn't make sense to me. First, consider a backward pde $v_t+v_{xx}=0$, which doesn't satisfy that condition. But having a change of variables as $u:=e^{ct}v,c<0$ I have an equation for $u$: $u_t+u_{xx}-cu=0$ which satisfies the condition and then there is existence. But the two equations are equivalent up to a change of variables so they both either have it or not. Another argument, we trivially know that heat equation, can be viewed as a degenerate elliptic equation and has a solution but does't not satisfy the property of having $c\leq c_0<0$.
Mar
11
comment Existence of the degenerate elliptic PDE coefficient condition
So, coefficient $c$ affects coercivity? Isn't it a property of the coefficint in front of the second order operator? I have looked at your answer, I don't think it is related to my question as I rather have issues with understanding of the existence of the solutions to the basic elliptic and parabolic equations, just don't have any other book on parabolic equations at hands right now.
Mar
11
comment Existence of the degenerate elliptic PDE coefficient condition
But, coercivity is the condition for $a$, or $c$ would affect that as well? I can refer to the book I am reading: Olejnik and Radkevic: Second order equations with nonnegative characteristic form. Paragraph 5. Theorem on existence, I did not get into the proof really, the idea is to do the elliptic regularization, that is add $\epsilon \sum u_{x_ix_j}$ and then use the regular elliptic theory for strongly elliptic equations with $\tilde{a}\geq a_0>0$. The book considers the more general $c=c(x)$, but we can just think of it as a constant to put some contraints on it in order to have existence.
Mar
11
asked Existence of the degenerate elliptic PDE coefficient condition
Mar
5
comment ratio zero over zero uncertainty
Both answers are good. That was the first though. Thanks!
Mar
5
accepted ratio zero over zero uncertainty
Mar
5
asked ratio zero over zero uncertainty
Feb
15
accepted partial derivative of $L^2$ norm?
Feb
15
awarded  Critic
Feb
15
asked partial derivative of $L^2$ norm?
Feb
14
comment monotone Hermite interpolation
your answers are very helpful. Thanks a lot!
Feb
14
accepted monotone Hermite interpolation